Geo5.3.35

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Find the equation of the hyperbola whose asymptotes are 7x+5y-3=0,2x+4y+1=0\, and passing thro' (-2,1)\,

Given asymptotes are 7x+5y-3=0,2x+4y+1=0\,

The equation of the parabola is (7x+5y-3)(2x+4y+1)+\lambda =0\,

Given that the hyperbola passes through (-2,1)\,

(-14+5-3)(-4+4+1)+\lambda =0,\lambda =12\,

Therefore the equation of the hyperbola is (7x+5y-3)(2x+4y+1)+12=0\,

14x^{2}+28xy+7x+10xy+20y^{2}+5y-6x-12y-3+12=0\,

14x^{2}+38xy+20y^{2}+x-7y+9=0\,


Main Page:Geometry:Hyperbola